Global prior distributions for the analysis of discrete graphical models

We propose a new class of prior distributions for the analysis of discrete graphical models. Such a class, obtained following a conditional approach, generalizes the hyper Dirichlet distributions of Dawid and Lauritzen (1993), since it can be extended to non decomposable graphical models. The two classes are compared in terms of model selection, with an application to a medical data-set illustrating the performance of the two resulting procedures. The proposed class turns out to select simpler, more parsimonious structures.